Numerical algorithm for the time dependent strongly-out-of-equilibrium Boltzmann equation: high dimensional Gauss integration
This thesis focuses on substituting the current Monte Carlo method with Gauss integration, which adapts to the geometry of the problem, to solve the collision term of Boltzmann equation. The scattering integral is first derived from the time dependent Boltzmann equation for the study of electroni...
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| Format: | Final Year Project |
| Language: | English |
| Published: |
Nanyang Technological University
2022
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| Online Access: | https://hdl.handle.net/10356/157010 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | This thesis focuses on substituting the current Monte Carlo method with Gauss
integration, which adapts to the geometry of the problem, to solve the collision
term of Boltzmann equation. The scattering integral is first derived from the time
dependent Boltzmann equation for the study of electronic population in stronglyout-
of-equilibrium solids. Next, Gauss points of the Cartesian product of simplexes
are constructed using C++ to solve the scattering integral with Gauss integration.
Comparing the new Gauss integration with the Monte Carlo method, it was found
that Gauss integration can produce an accurate result in a shorter period of time,
which is sufficient to replace the Monte Carlo method in solving the problem.
Lastly, this new method was used in application to graphene to compute the thermalisation
of electrons in scattering. |
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